A tank has a total capacity of 100 L, but initially it contains 15 L of pure water.Water flows into the tank 8 L per minute and contains 2 kg of salt. The solutionin the tank is being mixed well. If the well-mixed solution in the tank exits 7 Lper minute:a) show how the differential equation below describes the concentration of Sin the solution at any time t?ds75= 16t - 15dtb) determine the amount of salt (kilograms) in the solution just before thetank overflows. Express your answers accurate to four decimal places.

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Answered: A tank has a total capacity of 100 L,…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Please solve and explain this differential equ
Newton's Law of Cooling states that the rate at which the temperature of a cooling object decreases and the rate at which a warming object increases are proportional to the difference between the temperature of the object and the temperature of the surrounding medium. The differential equation formula is given as: dT = k (T – A) dt - T = temperature of object at time t А ambient temperature (aka temperature of the surrounding medium) k = constant of proportionality Okay, now here's the problem. A glass of delicious orange soda (with an initial temperature of 34°F) is placed in a room with a constant temperature of 72°F. One hour later, the temperature of the orange soda is 52°F. Find the exact simplified value of k. Hint: solve the differential equation for T and note that A is a constant.
A 90 gallon tank initially contains 10 gallons of water and 5 pounds of salt. Salt solution, at 2.5 lb/gal, begins entering the tank at a rate of 4 gal/min. Simultaneously, a 3 gal/min drain is opened. in the bottom of the tank. Let s(t) be the amount of salt in the tank at time t. Find the differential equation and initial condition for which s(t) is a solution. DO NOT SOLVE THE DIFFERENTIAL EQUATION.
Tank A initially contains 500 Litres of a brine solution with a concentration of 0.5 kg perlitre and tank B contains 500 Litres of water. Solution is pumped from tank A to tank B ata rate of 4 Litres /min and from tank B to tank A at a rate of 8 Litres /min. The tanks are keptwell stirred. Let the number of kilograms of salt in tank A be A1 after t minutes and B1in tank B.(a) Write down equations showing, respectively, the concentrations C1 and C2 inthe tanks after t minutes.(b) Write down two differential equations to show how A1 and B1 vary with time.(c) What is the relation between A1 and B1?(d) Eliminate B1 between the two equations in (b) and solve the resulting equationfor A1.(e) What is the concentration in tank A after 10 minutes?
Please help for c and d.
please show work
A large tank is filled to capacity with 700 gallons of pure water. Brine containing 3 pounds of salt per gallon is pumped into the tank at a rate of 7 gal/min. The well-mixed solution is pumped out at a rate of 14 gals/min. (a) Write a differential equation and the initial condition for A, the number of pounds of salt in the tank, at time t. Show your construction step-by-step with verbal explanations. Include the discovery of • how many pounds of salt is pumped in per minute. • the volume of solution in the tank at time t, the concentration (pound per gallon) of salt in the tank at time t expressed in terms of both A and t, how much salt is pumped out per minute, also expressed in terms of A and t, (b) Solve the differential equation to find A(t), the amount of salt in the tank at time t.
A 50 gallon tank is full to the brim with pure water, and 5 gallons/minute of a brine solution with 0.3 kg/gallon salt flows into it. Since the tank is full, 5 gallons/minute of well-mixed solution flows onto the ground. Find a differential equation with initial condition for S(t) = number of kg salt in the tank and solve it for S(t).
A tank originally contains 120 litre of brine with a salt concentration of 4 gram of salt per litre. Then brine with 15 gram of salt per litre is poured into the tank at a rate of 6 litre/minute, and the well-stirred mixture is allowed to leave at the same rate. a. Model this situation by a differential equation with initial conditions. b. Find the concentration of salt in the tank after 20 minutes. c. Find the eventual concentration of salt in the tank. (Hint: The eventual value will be as time goes to infinity.)
Need as soon as possible pls. Thank you.
A tank initially contains 200L of pure water. Salt enters into the solution constantly 5 kilograms for every minute, then will be mixed well into the contents of the tank. If the well-mixed solution exits from the tank at the rate 10 L per minute, show how the differential equation below describes the salt concentration S in the solution at any time t. ds :5 t - 20 %3! dt

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